Answer:
XZ ≈ 13.86
Step-by-step explanation:
To find the length of the altitude XZ , we can use the Geometric Mean Theorem, which states that the ratio of one segment to the altitude is equal to the the ratio of the altitude to the other segment.
In the right triangle WXY the altitude XZ is drawn from the right angle to the hypotenuse, dividing the hypotenuse into two segments WZ and YZ.
Then
[tex]\frac{WZ}{XZ}[/tex] = [tex]\frac{XZ}{YZ}[/tex] ( substitute values )
[tex]\frac{12}{XZ}[/tex] = [tex]\frac{XZ}{16}[/tex] ( cross multiply )
XZ² = 12 × 16 = 192 ( take square root of both sides )
[tex]\sqrt{XZ^2}[/tex] = [tex]\sqrt{192}[/tex]
XZ = [tex]\sqrt{192}[/tex] ≈ 13.86 ( to the nearest hundredth )
